Q1  Aspden's unit energies (Part 1 chain; POC ch. 7)
  1    quon rest energy m0 c^2 (7.25)                                             = 0.0407813 m_e  = 0.0208392 MeV 
  1    electron                                                                   = 1.0 m_e  = 0.510999 MeV 
  1    27 quons (photon unit, rest energy)                                        = 1.1011 m_e  = 0.562659 MeV 
  1    half the cell energy, E0/2 (his 'virtual muon')                            = 206.333 m_e  = 105.436 MeV 
  1    cell energy E0 (7.29), his 'virtual muon pair'                             = 412.666 m_e  = 210.872 MeV 
  1    E0/3                                                                       = 137.555 m_e  = 70.2906 MeV 
  1    N = 1843 electron masses (quon/electron charge-volume ratio)               = 1843.0 m_e  = 941.771 MeV 
  1    graviton, 5063 electron masses (Tutorial Notes 6 and 16)                   = 5063.0 m_e  = 2587.19 MeV 

Q2  Quark masses
  1    PDG 2024 current mass u (MS-bar, 2 GeV)                                    = 2.16 MeV
  1    PDG 2024 current mass d (MS-bar, 2 GeV)                                    = 4.7 MeV
  1    PDG 2024 current mass s (MS-bar, 2 GeV)                                    = 93.5 MeV
  1    PDG 2024 current mass c (MS-bar, m_c)                                      = 1273.0 MeV
  1    PDG 2024 current mass b (MS-bar, m_b)                                      = 4183.0 MeV
  1    PDG 2024 current mass t (direct)                                           = 172570.0 MeV
  2    u, d (constituent, from the proton's magnetic moment, m_p/mu_p)            = 335.955 MeV
  2    s (constituent, from the Lambda's magnetic moment)                         = 510.208 MeV
  2    c (half the J/psi mass, 3096.900/2)                                        = 1548.45 MeV
  2    b (half the Upsilon(1S) mass, 9460.40/2)                                   = 4730.2 MeV
  3    QCD scale Lambda (MS-bar, 5 flavours) from alpha_s(M_Z) = 0.1180, at 2, 3, 4 loops; convention-dependent = 226.235, 208.367, 208.365 MeV (larger for fewer flavours) 

Q3  Each Aspden energy against the nearest quark mass (current and constituent lists together)
  1    quon rest energy m0 c^2 (7.25)               vs u (MS-bar, 2 GeV)          = ratio 0.0096478 
  1    electron                                     vs u (MS-bar, 2 GeV)          = ratio 0.23657 
  1    27 quons (photon unit, rest energy)          vs u (MS-bar, 2 GeV)          = ratio 0.26049 
  1    half the cell energy, E0/2 (his 'virtual muo vs s (MS-bar, 2 GeV)          = ratio 1.1277 
  1    cell energy E0 (7.29), his 'virtual muon pai vs u, d (constituent, from    = ratio 0.62768 
  1    E0/3                                         vs s (MS-bar, 2 GeV)          = ratio 0.75177 
  1    N = 1843 electron masses (quon/electron char vs c (MS-bar, m_c)            = ratio 0.7398 
  1    graviton, 5063 electron masses (Tutorial Not vs b (MS-bar, m_b)            = ratio 0.6185 

Q4  Look-elsewhere: chance that an arbitrary energy lands within a given distance of one of these quark masses
  1    within +-1%: chance per energy; expected hits from 8 energies; hits found  = 0.0118; 0.0947; 0 
  1    within +-2%: chance per energy; expected hits from 8 energies; hits found  = 0.0236; 0.188; 0 
  1    within +-5%: chance per energy; expected hits from 8 energies; hits found  = 0.058; 0.464; 0 

Q5  Quon and quark, property by property
  1    charge: quon (Aspden) / up quark / down quark                              = e / +2e/3 / -e/3 
  2    rest energy: quon / up quark (current) / up quark (constituent)            = 20.8392 keV / 2160 keV / 335955.0 keV 
  3    ratio, up-quark current mass / quon                                        = 103.651 
  4    size: quon charge radius b (7.15) / proton charge radius (CODATA 2022)     = 23.0329 fm / 0.84075 fm 
  5    quark-quark contact scale, LHC dijets (PDG 2024 compositeness review), TeV; hbar c / Lambda in m = 9.2-29.5; 6.7e-21-2.1e-20 
  5    lepton-quark contact scale, LHC dileptons (same review), TeV; hbar c / Lambda in m = 23.9-36.0; 5.5e-21-8.3e-21 
  6    number density: quons fill space at 1/d^3                                  = 3.86151e+36 per m^3 
  7    quarks: confined, three valence quarks per nucleon; PDG: free-quark searches since 1977 all negative =  

Q6  Sizes: charge spheres of Thomson radius 2e^2/(3 m c^2) against measurement
  1    electron: Aspden's charge radius                                           = 1.87863 fm   measured: point-like; no structure seen in e+e- scattering at LEP up to 209 GeV 
  1    muon: Aspden's charge radius                                               = 0.00908566 fm   measured: point-like 
  1    proton: Aspden's charge radius                                             = 0.00102313 fm   measured: 0.84075 fm (CODATA 2022) 
  2    proton: measured radius / Aspden's core charge radius                      = 821.741 
  2b   his composite proton (core + electron + positron, 1969-80): each lepton sphere's radius vs the proton's = 1.87863 fm vs 0.84075 fm 
  3    electron as a thin charged shell of radius 1.879 fm (the most favourable case): q a at 100 GeV = 952.038 
  4      form factor sin(qa)/(qa) is at most 1/(qa)                               = 0.00105 
  5      large-angle e+e- (Bhabha) scattering, one factor per particle, squared: suppressed to at most (1/qa)^4 = 1.22e-12 
  5b     a uniformly filled sphere (Aspden 1972: 'a sphere filled by electric charge') falls faster, about 3/(qa)^2 = 3.31e-6 
  6      distance probed at 100 GeV, hbar c / q                                   = 1.97e-18 m

Q7  Fractional charge and colour: the ratio R = sigma(e+e- -> hadrons)/sigma(e+e- -> mu+mu-)
  1    R counts the squared charges of the quark types that can be made: R = (colours) x sum of q^2 =  
  2    fractional charges, 3 colours (quark model with QCD): R below charm, R above charm = 2.0, 3.333 
  2    fractional charges, no colour: R below charm, R above charm                = 0.6667, 1.111 
  2    integer charges, 3 colours (Han-Nambu 1965): R below charm, R above charm  = 4.0, 6.0 
  2    integer charge +-e for every quark, no colour: R below charm, R above charm = 3.0, 4.0 
  3    QCD correction factor (1 + alpha_s/pi) at about 3 GeV and at 10.5 GeV      = 1.07958, 1.06366 
  4    fractional, 3 colours, with the correction: R at 3.08 GeV, R at 10.52 GeV  = 2.15915, 3.54554 
  5    measured: BESIII 2022 at 3.0800 GeV (stat, syst)                           = 2.277 +- 0.003 +- 0.046 
  6    measured: CLEO 1998 at 10.52 GeV (stat, syst)                              = 3.56 +- 0.01 +- 0.07 
  7    only fractional charges with three colours fit both; integer-charge models give 3-4 below charm =  

Q8  Aspden's alternative: charges that are always +-e or 0 but average to 2/3 and -1/3 over time (ESR5 1994;
    commentary on 1986d). Scattering measures the average of the SQUARED charge, not the square of the average.
  1    for a charge that takes only the values -1, 0, +1: <q^2> = P(q not 0) >= |<q>| =  
  2    fixed fractional charges: <q^2> for u and d                                = 0.444444, 0.111111 
  3    flipping unit charges with the same averages: smallest possible <q^2> for u and d = 0.666667, 0.333333 
  4    electron/neutrino deep-inelastic ratio for an isoscalar target: fixed charges (the '5/18 rule') = 0.277778 
  5      the same with flipping unit charges: at least                            = 0.5 
  6      ratio of the two (the measured 'charge ratio' should be 1 for fixed fractional charges) = 1.8 
  7    measured charge ratio, CCFR/NuTeV with NMC, 0.1 < x < 0.4 (and after reanalysis down to x = 0.01) = 1 within 2-3% 
  8    R below charm with three colours and flipping charges: at least 3 x (2/3 + 1/3 + 1/3) = 4.0 
  9    Aspden has no colour: flipping charges without colour allow R from 4/3 to 3 below charm, 2 to 4 above =  
  10     measured 2.28 and 3.56 lie inside those ranges, so R alone does not exclude the flipping picture =  
  11   premise of the scattering argument: charges flip slower than the probe; his clock h/m_e c^2 vs hbar/Q at 2 GeV = 8.09e-21 s vs 3.3e-25 s 
  12   premise: neutrinos count his constituents as they count quarks (an assumption; he calls the neutrino illusory) =  

Q9  Aspden's 1980 'multiple charge quark' Z = 43 and MacGregor's quark masses (Physics Unified pp. 152-155)
  1    Z = nearest integer to sqrt(1843) and to sqrt(1836)                        = 42.9302, 42.8486 -> 43 
  2    43e quark in one electron volume, 43^2 m_e                                 = 1849.0 m_e = 944.837 MeV 
  3    after expanding to 43 electron volumes, 43^(5/3) m_e                       = 527.773 m_e = 269.692 MeV 
  4    43:42 pair, eq. (209), against MacGregor's S+ = 330.6 MeV                  = 330.581 MeV 
  5    43:43 pair, eq. (210)                                                      = 337.115 MeV 
  6    44:42 pair, eq. (211) as read, against MacGregor's S++ = 336.9 MeV (he prints 336.9) = 337.014 MeV 
  7    M+- = [(3/2)^(1/2) - 1] x 330.6, against MacGregor's 74.6 MeV              = 74.3007 MeV 
  8    M0 = (1/2)(273.126 + 1) m_e, against MacGregor's 70.0 MeV                  = 70.039 MeV 
  9    for comparison: m_e/alpha (MacGregor's '70 MeV quantum') and today's constituent u, d mass m_p/mu_p = 70.0253 MeV; 335.955 MeV 
